Ratio and Proportion
Model ratios, scaling, percentages, direct and inverse proportion, growth, decay and iteration.
How to prepare for the current TMUA
Secure the shared mathematical specification, practise application in unfamiliar settings, then make every Paper 2 implication and proof step explicit.
Core concepts
Concept 1
Translate ratios into common multipliers or fractions of a whole.
Exam cue: Preserve the stated order of quantities in a ratio.
Concept 2
Represent direct and inverse proportion algebraically and graphically.
Exam cue: Test how one variable responds when the other doubles.
Concept 3
Use multiplicative change for scale effects, percentages, growth and decay.
Exam cue: Use one multiplier for each repeated percentage step.
Risk pitfalls and guardrails
Reversing the ratio order.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Assuming every increasing relationship is direct proportion.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Applying a length scale factor unchanged to area or volume.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Memory anchors
Ratio order
Match every number to the named order of quantities.
Direct
y = kx and y/x is constant.
Inverse
y = k/x and xy is constant.
Scale effects
Lengths scale by k, areas by k² and volumes by k³.
Percentage multiplier
Increase by r uses 1+r; decrease uses 1−r.
Iteration
Each output becomes the next input.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
A recipe uses flour:sugar=5:2. After adding 120 g sugar the ratio is 5:3. How much flour was present?
y is directly proportional to x² and y=45 when x=3. What is y when x=5?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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